Common zeros of two Bessel functions

Authors:
T. C. Benton and H. D. Knoble

Journal:
Math. Comp. **32** (1978), 533-535

MSC:
Primary 33A40; Secondary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1978-0481160-X

MathSciNet review:
0481160

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Abstract: There is a theorem that two Bessel functions and can have no common positive zeros if is an integer and where *m* is an integer, but this does not preclude the possibility that for unrestricted real positive and not differing by an integer, the two functions and can have common zeros. An example is found where two such functions have two positive zeros in common.

**[1]**R. P. Brent,*An algorithm with guaranteed convergence for finding a zero of a function*, Comput. J.**14**(1971), 422–425. MR**339475**, https://doi.org/10.1093/comjnl/14.4.422**[2]**W. GAUTSCHI, "Algorithm 236, Bessel functions of the first kind,"*Comm. ACM*, v. 7, 1964, pp. 479-480.**[3]**HARVARD COMPUTATION LABORATORY,*Tables of Bessel Functions*, 1947-1951 Annals, vols. III-XIV, Harvard Univ. Press, Cambridge, Mass.**[4]**F. W. J. Olver,*A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order*, Proc. Cambridge Philos. Soc.**47**(1951), 699–712. MR**43551****[5]***Bessel functions. Part III: Zeros and associated values*, Royal Society Mathematical Tables, Vol. 7. Prepared under the direction of the Bessel Functions Panel of the Mathematical Tables Committee, Cambridge University Press, New York, 1960. MR**0119441****[6]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR**0010746**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0481160-X

Article copyright:
© Copyright 1978
American Mathematical Society